The selection of the loss function to be optimized is crucial for the task of simplification since we seek for a balance between the preservation of the structure and the salient features. A major barrier of most common distance metrics is the uniform weighting of points that can not reflect the perceptual differences between objects. As shown in many studies [1]}, [2]}, [3]} the commonly used Chamfer distance (CD) between two point sets \(\mathcal {P}_1,\mathcal {P}_2\)  defined as:
\(d_{\mathcal {P}_1, \mathcal {P}_2} = \sum _{x \in \mathcal {P}_1} \min _{y \in \mathcal {P}_2} \Vert  x-y \Vert ^2 + \sum _{y \in \mathcal {P}_2} \min _{x \in \mathcal {P}_1} \Vert x-y \Vert ^2\) 
